Asked by melvin kgole on Apr 27, 2024
Verified
Your home is on a square lot. To add more space to your yard, you purchase an additional 30 feet along the side of your property (see figure) . The area of the lot is now 43,875 square feet. What are the dimensions of the new lot?
A) 180 feet by 210 feet
B) 180 feet by 240 feet
C) 165 feet by 195 feet
D) 195 feet by 225 feet
E) 225 feet by 420420420 feet
Square Lot
In geometry, a square-shaped plot of land.
Additional Space
Extra or unused space provided beyond what is necessary.
- Resolve issues concerning the geometric uses of quadratic functions, including calculations of area and perimeter.
Verified Answer
SD
Sylvia DooleyMay 04, 2024
Final Answer :
D
Explanation :
Let x be the length of each side of the original square lot.
The area of the original lot is x^2.
When 30 feet is added to one side, the new length of that side becomes x + 30.
The area of the new lot is 43,875 square feet.
Thus, we have the equation:
(x + 30)^2 = 43,875
Simplifying, we get:
x + 30 = ±sqrt(43,875)
x + 30 ≈ ±209.2
x ≈ -30 + 209.2 or x ≈ -30 - 209.2 (we reject the negative solution)
Therefore, x ≈ 179.2
The new dimensions of the lot are (x + 30) by x, which is approximately 209.2 feet by 179.2 feet.
The closest option is D, which is 195 feet by 225 feet.
The area of the original lot is x^2.
When 30 feet is added to one side, the new length of that side becomes x + 30.
The area of the new lot is 43,875 square feet.
Thus, we have the equation:
(x + 30)^2 = 43,875
Simplifying, we get:
x + 30 = ±sqrt(43,875)
x + 30 ≈ ±209.2
x ≈ -30 + 209.2 or x ≈ -30 - 209.2 (we reject the negative solution)
Therefore, x ≈ 179.2
The new dimensions of the lot are (x + 30) by x, which is approximately 209.2 feet by 179.2 feet.
The closest option is D, which is 195 feet by 225 feet.
Learning Objectives
- Resolve issues concerning the geometric uses of quadratic functions, including calculations of area and perimeter.